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I enter x^* to typeset x*, but get an error message. Why?

The problem is that * is a binary operator, that is
there has to be an expression on both sides of the symbol.

You either have to enter the expression x^{{}*{}} to avoid the
error message, or you could type x^"*" as well, where the quotes
will interprete the asterisk not as a binary operator but as a "standalone" symbol.

This answer applies to a lot of other symbols as well. Some operators, such as +, are unary, that is there only has to be an expression to the right of the symbol. To typeset x+ you can enter x^{+{}}< or, of course, x^"+".

When I enter one of the symbols #, & ,|,^ or _ I get an unexpected result or an error message. How can I use these symbols?

These symbols all have a special meaning in Math:

The symbol # is used in stacks and matrices.

The symbols & and | are used for logical and and logical or.

The symbols ^ and _ are used for subscripts and superscripts.

To use them in your formula you can put them in quotation marks,
which means that you insert them as text.

If you want to use the symbol "|" you should consider
whether the construction you need is one of the the following:

a divides b is used to typeset a| b.

abs a is used to typeset |a|.

When I enter 3xy the number 3 comes out in italics. Is this a bug?

Not really. What happens here is, that Math uses multi-letter
variables, which are common in some disciplines, like economics. The
rule is that a variable consists of a sequence of letters, numbers
and dots (the first character can not be a dot).

So when you enter 3xy this is considered a variable - and
variables are typeset in italics. The only odd thing here is, that a
variable can start with a number.

The correct way to enter the expression if you mean 3 times x
times y is 3 x y (with spaces between the characters).

I want to use a binary operator (like union orotimes) as a large operator (like int or sum). How can I do that?

You have to define the symbol you want to use as a user-defined
symbol first. See <A HREF="012.html">FAQ #012</A> for instructions;
most of the symbols used by Math are part of the StarMath
font.

Let's say you have defined the union symbol as the user-defined
symbol %union. You can then enter for example

oper%union from i in I A_i

in order to typeset the formula

Note: In build 633 this doesn't work if there is a space before
%union (this is a bug in the parser).

Any user-defined symbol can be used as a large operator if it is
preceded with oper as in the example.